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# how would i solve this

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How many of the first 500 positive integers are multiples of integers 3, 4 or 5?

May 24, 2024

#1
+713
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We can find the count of multiples of 3, 4 and 5 upto 500 using the following logic. We iterate through all numbers from 1 to 500 and check if the number is divisible by 3, 4 or 5. If the number is divisible by any of these numbers, we increment the count.

Here's the code for this logic:

Python

# Count multiples of 3, 4, and 5 up to 500 count = 0 # Iterate through the first 500 positive integers for num in range(1, 501): # Check if the number is a multiple of 3, 4, or 5 if num % 3 == 0 or num % 4 == 0 or num % 5 == 0: count += 1 print(count)

This code outputs the following:

320

There are total 320 multiples of 3, 4 or 5 up to 500.

May 24, 2024
#3
+1332
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I think there was a slight error in your code for python.

I followed your logic and iteration, and the answer turned out to be 300.

I don't know if I made an error, but it does match with the answer I got using plain logic.

Here's my explenation for the problem.

First, let's find how many of each number there are.

500/3 = 166.66, so there are 166 integers.

500/4 = 125, so there are 125 integers.

500/5 = 100, so there are 100 integers.

Next, we must find the duplicates of numbers.

3*4 = 12

3*5 = 15

4*5 = 20

500/12 = 41.67, so there are 41 integers

500/15 = 33.33, so there are 33 itnegers.

500/20 = 25, so there are 25 integers.

LCM = 3*4*5 = 60.

500/60 = 8.33, so there are 8 integers.

166+125+100-41-33-25+8 = 300.

Let me summarize.

First, we find how many numbers are divisble by 3,4,5. However, there are duplicates, so we subtract those, before adding the LCM!

Thanks! :)

NotThatSmart  May 24, 2024
#2
+1332
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First, let's find how many of each number there are.

500/3 = 166.66, so there are 166 integers.

500/4 = 125, so there are 125 integers.

500/5 = 100, so there are 100 integers.

Next, we must find the duplicates of numbers.

3*4 = 12

3*5 = 15

4*5 = 20

500/12 = 41.67, so there are 41 integers

500/15 = 33.33, so there are 33 itnegers.

500/20 = 25, so there are 25 integers.

LCM = 3*4*5 = 60.

500/60 = 8.33, so there are 8 integers.

166+125+100-41-33-25+8 = 300.

Let me summarize.

First, we find how many numbers are divisble by 3,4,5. However, there are duplicates, so we subtract those, before adding the LCM!

Thanks! :)

May 24, 2024